Let be one of the Atkin–Lehner quotients of a curve such that has genus and its Jacobian variety is absolutely simple. We show that the Shafarevich–Tate group is trivial. This verifies the strong BSD conjecture for .
Soit un des quotients d’Atkin–Lehner d’une courbe tel que est de genre et sa jacobienne est absolument simple. On démontre que le groupe de Shafarevich–Tate est trivial. Ceci vérifie la conjecture BSD forte pour .
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Timo Keller 1; Michael Stoll 1
@article{CRMATH_2022__360_G5_483_0, author = {Timo Keller and Michael Stoll}, title = {Exact verification of the strong {BSD} conjecture for some absolutely simple abelian surfaces}, journal = {Comptes Rendus. Math\'ematique}, pages = {483--489}, publisher = {Acad\'emie des sciences, Paris}, volume = {360}, year = {2022}, doi = {10.5802/crmath.313}, language = {en}, }
TY - JOUR AU - Timo Keller AU - Michael Stoll TI - Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces JO - Comptes Rendus. Mathématique PY - 2022 SP - 483 EP - 489 VL - 360 PB - Académie des sciences, Paris DO - 10.5802/crmath.313 LA - en ID - CRMATH_2022__360_G5_483_0 ER -
Timo Keller; Michael Stoll. Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 483-489. doi : 10.5802/crmath.313. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.313/
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